We present a Gaussian ensemble of random cyclic matrices on the real field and study their spectral fluctuations. These cyclic matrices are shown to be pseudosymmetric with respect to generalized parity. We calculate the joint probability distribution function of eigenvalues and the spacing distributions analytically and numerically. For small spacings, the level spacing distribution exhibits either a Gaussian or a linear form. Furthermore, for the general case of two arbitrary complex eigenvalues, leaving out the spacings among real eigenvalues, and, among complex conjugate pairs, we find that the spacing distribution agrees completely with the Wigner distribution for a Poisson process on a plane. The cyclic matrices occur in a wide variety of physical situations, including disordered linear atomic chains and the Ising model in two dimensions. These exact results are also relevant to two-dimensional statistical mechanics and $\nu$-parametrized quantum chromodynamics.

Several results concerning active media or metamaterials are proved and discussed. In particular, we consider the permittivity, permeability, wave vector, and refractive index, and discuss stability, refraction, gain, and fundamental limitations resulting from causality.

The dynamical phase diagram of the fractional Langevin equation is investigated for a harmonically bound particle. It is shown that critical exponents mark dynamical transitions in the behavior of the system. Four different critical exponents are found. (i) ${\alpha }_c=0.402\pm 0.002$ marks a transition to a nonmonotonic underdamped phase, (ii) ${\alpha }_R=0.441\dots$ marks a transition to a resonance phase when an external oscillating field drives the system, and (iii) ${\alpha }_{{\chi }_1}=0.527\dots$ and (iv) ${\alpha }_{{\chi }_2}=0.707\dots$ mark transitions to a double-peak phase of the “loss” when such an oscillating field present. As a physical explanation we present a cage effect, where the medium induces an elastic type of friction. Phase diagrams describing over and underdamped regimes, with or without resonances, show behaviors different from normal.

Information flow or information transfer is an important concept in general physics and dynamical systems which has applications in a wide variety of scientific disciplines. In this study, we show that a rigorous formalism can be established in the context of a generic stochastic dynamical system. An explicit formula has been obtained for the resulting transfer measure, which possesses a property of transfer asymmetry and, if the stochastic perturbation to the receiving component does not rely on the giving component, has a form the same as that for the corresponding deterministic system. This formula is further illustrated and validated with a two-dimensional Langevin equation. A remarkable observation is that, for two highly correlated time series, there could be no information transfer from one certain series, say $x_2$, to the other $\left(x_1\right)$. That is to say, the evolution of $x_1$ may have nothing to do with $x_2$, even though $x_1$ and $x_2$ are highly correlated. Information flow analysis thus extends the traditional notion of correlation analysis and/or mutual information analysis by providing a quantitative measure of causality between dynamical events.

Quantum corrections to the noninertial Brownian motion of a particle in a one-dimensional tilted cosine periodic potential are treated in the high-temperature and weak bath-particle coupling limit by solving a quantum Smoluchowski equation for the time evolution of the distribution function in configuration space. The theoretical predictions from two different forms of the quantum Smoluchowski equation already proposed—viz., J. Ankerhold et al. [Phys. Rev. Lett. 87, 086802 (2001)] and W. T. Coffey et al. [J. Phys. A 40, F91 (2007)]—are compared in detail in a particular application to the dynamics of a point Josephson junction. Various characteristics (stationary distribution, current-voltage characteristics, mean first passage time, linear ac response) are evaluated via continued fractions and finite integral representations in the manner customarily used for the classical Smoluchowski equation. The deviations from the classical behavior, discernible in the dc current-voltage characteristics as enhanced current for a given voltage and in the resonant peak in the impedance curve as an enhancement of the $Q$ factor, are, respectively, a manifestation of relatively high-temperature nondissipative tunneling (reducing the barrier height) and dissipative tunneling (reducing the damping of the Josephson oscillations) near the top of a barrier.

We investigate the possibility of an Anderson-type transition in the quantum kicked rotor with a smooth potential due to dynamical localization of the wave functions. Our results show the typical characteristics of a critical behavior, i.e., multifractal eigenfunctions and a scale-invariant level statistics at a critical kicking strength which classically corresponds to a mixed regime. This indicates the existence of a localization to delocalization transition in the quantum kicked rotor. Our study also reveals the possibility of other types of transition in the quantum kicked rotor, with a kicking strength well within the strongly chaotic regime. These transitions, driven by the breaking of exact symmetries, e.g., time reversal and parity, are similar to weak-localization transitions in disordered metals.

The spectral density of various ensembles of sparse symmetric random matrices is analyzed using the cavity method. We consider two cases: matrices whose associated graphs are locally treelike, and sparse covariance matrices. We derive a closed set of equations from which the density of eigenvalues can be efficiently calculated. Within this approach, the Wigner semicircle law for Gaussian matrices and the Marčenko-Pastur law for covariance matrices are recovered easily. Our results are compared with numerical diagonalization, showing excellent agreement.

We present an explicit theory of the degradation and thermal fragmentation kinetics of polymerlike systems and aggregates with multiple bonds in the presence of stochastic evaporation and condensation (restoration) of bonds. The analysis is conducted on the basis of the determination of the first passage time to state zero (fragmented state) in the Ehrenfest diffusion model in continuous time. The main approximations of the developed theory include the assumption that multiple bonds in any link between the primary elements in the aggregate do not interact with each other and that the coagulation rate after thermal fragmentation of the aggregates is negligible (which gives the absorbing zero state in the Ehrenfest model). In particular, it is demonstrated that even small condensation rates (of $\sim 10$ times smaller than the rates of bond evaporation) may have a significant effect on typical evolution times for the degrading aggregates and can result in a strong accumulation of nanoaggregates in the intermediate fragmentation modes. The simple asymptotic (predominantly exponential) behavior of the obtained solution at large evolution times is analyzed and discussed. The results will be important for the investigation of the degradation kinetics of a variety of polymerlike systems with multiple bonds, including self-arranged structures, polymer networks, different types of nanoclusters and their thermal fragmentation, etc.

We use a molecular dynamics model to simulate the formation and evolution of a granular pile in two dimensions in order to gain a better understanding of the role of magnetic interactions in avalanche dynamics. We find that the angle of repose increases only slowly with magnetic field; the increase in angle is small even for intergrain cohesive forces many times stronger than gravity. The magnetic forces within the bulk of the pile partially cancel as a result of the anisotropic nature of the dipole-dipole interaction between grains. However, we show that this cancellation effect is not sufficiently strong to explain the discrepancy between the angle of repose in wet systems and magnetically cohesive systems. In our simulations we observe shearing deep within the pile, and we argue that it is this motion that prevents the angle of repose from increasing dramatically. We also investigate different implementations of friction with the front and back walls of the container, and conclude that the nature of the friction dramatically affects the influence of magnetic cohesion on the angle of repose.

We investigate magnetic-field-induced changes on transmitted light intensity in a magnetic disordered phase of iron oxide nanoparticle suspension. We observe a dramatic decrease in the transmitted light intensity at a critical magnetic field. The critical magnetic field follows power-law dependence with the volume fraction of the nanoparticles suggesting a disorder-order structural transition. The light intensity recovers fully when the magnetic field is switched off. We discuss the possible reasons for the reduction in the light intensity under the influence of magnetic field. Among the various mechanisms such as Kerker’s condition for zero forward scattering, Faraday effect, Christiansen effect, photoinduced refractive index mismatch between the two components of the dispersion, etc., the resonances within the magnetic scatterers appear to be the plausible cause for the extinction of light. The circular pattern observed on a screen placed perpendicular to the incident beam confirms the formation of rodlike structures along the direction of propagation of the light.

I present a theoretical investigation of the temperature and magnetic field dependence of isotropic (paranematic) wetting layers close to an aligning substrate within a semi-infinite nematic liquid crystal with positive magnetic anisotropy under condition of weak homeotropic anchoring. Using the Landau–de Gennes model supplement by Nobili-Durand surface free energy, the existence and stability of paranematic wetting layers close to the substrate and below the nematic-isotropic temperature are discussed. Numerical results are presented showing the phase diagram for the isotropic (paranematic), nematic, and wetting layer states. In the present work, the dependence of the transition kind to the magnetic field is discussed.

Group theoretical arguments combined with normal mode analysis techniques are applied to a coarse-grained approximation of icosahedral viral capsids which incorporates areas of variable flexibility. This highlights a remarkable structure of the low-frequency spectrum in this approximation, namely, the existence of a plateau of 24 near zero modes with universal group theory content.

We introduce a minimal model description for the dynamics of transcriptional regulatory networks. It is studied within a mean-field approximation, i.e., by deterministic ODE’s representing the reaction kinetics, and by stochastic simulations employing the Gillespie algorithm. We elucidate the different results that both approaches can deliver, depending on the network under study, and in particular depending on the level of detail retained in the respective description. Two examples are addressed in detail: The repressilator, a transcriptional clock based on a three-gene network realized experimentally in E. coli, and a bistable two-gene circuit under external driving, a transcriptional network motif recently proposed to play a role in cellular development.

We present a kinetic Monte Carlo method for simulating chemical transformations specified by reaction rules, which can be viewed as generators of chemical reactions, or equivalently, definitions of reaction classes. A rule identifies the molecular components involved in a transformation, how these components change, conditions that affect whether a transformation occurs, and a rate law. The computational cost of the method, unlike conventional simulation approaches, is independent of the number of possible reactions, which need not be specified in advance or explicitly generated in a simulation. To demonstrate the method, we apply it to study the kinetics of multivalent ligand-receptor interactions. We expect the method will be useful for studying cellular signaling systems and other physical systems involving aggregation phenomena.

Translocation of a single-stranded DNA molecule through genetically engineered $\alpha$-hemolysin channels with positively charged walls is studied. It is predicted that transport properties of such channels are dramatically different from neutral wild-type $\alpha$-hemolysin channels. We assume that the wall charges compensate a fraction $x$ of the bare charge $q_b$ of the DNA piece residing in the channel. Our predictions are as follows. (i) At small concentration of salt the blocked ion current decreases with $x$. (ii) The effective charge $q_s$ of the DNA piece, which is very small at $x=0$ (neutral channel) grows with $x$ and at $x=1$ reaches $q_b$. (iii) The rate of DNA capture by the channel grows exponentially with $x$. Our theory is also applicable to translocation of a double-stranded DNA molecular in narrow solid state nanopores with positively charged walls.

It is shown on the basis of scaling arguments that a disordered interface between two elastic solids will quite generally exhibit static and dry friction (i.e., kinetic friction which does not vanish as the sliding velocity approaches zero) because of Tomlinson-model instabilities that occur for small-length-scale asperities. This provides a possible explanation for why static and dry friction are virtually always observed, and superlubricity almost never occurs.

The synchronization of bursting Hindmarsh-Rose neurons coupled by a time-delayed fast threshold modulation synapse was studied. It is shown that there is a domain of the coupling parameter and nonzero time-lag values such that the bursting neurons are exactly synchronized. Furthermore, and contrary to the case of electrical synapses, such synchronous bursting is stochastically stable.

We consider a behavior of the zero Lyapunov exponent in the vicinity of the bifurcation point that occurs as the result of the interplay between dynamical mechanisms and random dynamics. We analytically deduce the laws for the dependence of this Lyapunov exponent on the control parameter both above and below the bifurcation point. The developed theory is applicable both to the systems with the random force and to the deterministic chaotic oscillators. We find an excellent agreement between the theoretical predictions and the data obtained by means of numerical calculations. We also discuss how the revealed regularities are expected to take place in other relevant physical circumstances.

Flows of dense emulsions show many complex features among which long range nonlocal effects pose a problem for macroscopic characterization. In order to get around this problem, we study the flows of several dense emulsions, with droplet size ranging from $0.3\text{to}40\mu \mathrm{m}$, in a wide-gap Couette geometry. We couple macroscopic rheometric experiments and local velocity measurements through magnetic resonance imaging (MRI) techniques. As concentration heterogeneities are expected in the wide-gap Couette flows of multiphase materials, we also designed a method to measure the local droplet concentration in emulsions with a MRI device. In contrast to dense suspensions of rigid particles where very fast migration occurs under shear in wide-gap Couette flows, we show that no migration takes place in dense emulsions even for strains as large as 100 000 in our systems. As a result of the absence of migration and of finite size effect, we are able to determine very precisely the local rheological behavior of several dense emulsions. As the materials are homogeneous, this behavior can also be inferred from purely macroscopic measurements. We thus suggest that properly analyzed purely macroscopic measurements in a wide-gap Couette geometry can be used as a tool to study the local constitutive laws of dense emulsions. All behaviors are basically consistent with Herschel-Bulkley laws of index 0.5. The existence of a constitutive law accounting for all flows contrasts with previous results obtained within a microchannel by Goyon et al. [Nature (London) 454, 84 (2008)]: the use of a wide-gap Couette geometry is likely to prevent here from nonlocal finite size effects; it also contrasts with the observations of Bécu et al. [Phys. Rev. Lett. 96, 138302 (2006)]. We also evidence the existence of discrepancies between a perfect Herschel-Bulkley behavior and the observed local behavior at the approach of the yield stress due to slow shear flows below the apparent yield stress in the case of a strongly adhesive emulsion.